What is the directrix-y^2=6y+x ?

The directrix-y^2=6y+x is x= 37/4

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directrix-y^2=6y+x

directrix

- y^{2} = 6 y + x

x = \frac{37}{4}

Solution steps

Rewrite

- y^{2} = 6 y + x

in the standard form

4 (- \frac{1}{4}) (x - 9) = (y - (- 3))^{2}

(h, k) = (9, - 3), p = - \frac{1}{4}

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(9, - 3)

x-coordinate

x = 9 - p

x = 9 - (- \frac{1}{4})

Refine

x = \frac{37}{4}

x = - \frac{1}{20} (y + 6)^{2} - 7

\frac{y ^{2} + 12 y + 36}{60}

(x - 5)^{2} - 1

- 2 x^{2} + 4 x - 2

- x^{2} + 150 x - 2000